International Journal of Engineering Trends and Technology (IJETT) – Volume 30 Number 2 - December 2015
Vehicle Active Suspension System performance using
Different Control Strategies
Atef, Mahmoud M #1, Soliman, M-Emad S.*2, Sharkawy, A.B. #3
Department of Mechanical Engineering, Assuit University, Egypt.
Abstract: The objective of the present work is to
investigate the performance of an active suspension
system of a typical passenger car through the
application of three different control strategies
under three different road irregularities. Tested
control strategies are PID, LQR and FLC. Road
irregularities considered are: a single rectangular
pothole, a single cosine bump, and an ISO class-A
random road disturbance. A 2-DOF quarter-vehicle
model is used to simulate, evaluate and compare
performance of these controllers against each other
and against the original passive suspension system.
Both tire gripping force and actuator force were
normalized with respect to vehicle weight to
recognize tire separation and enhance readability
and interpretation of results. Simulation results
showed that, active suspension systems are
advantageous compared to passive ones. Active
suspension implementing FLC control surpassed
both PID and LQR controllers. Improvement of ride
comfort was recognized by a reduction of sprung
mass displacement and acceleration up to 23.8%
and 52% respectively compared to the passive case.
Improvement of load capacity is clear with a
suspension travel reduction up to 61%. Moreover,
vehicle stability was enhanced by increasing the tire
separation margin up to 28 % of vehicle weight. An
actuator force up to 39.5% of vehicle weight is
required. All achieved by active suspension
implementing FLC control.
Keywords: - Vehicle active suspension system,
FLC, PID, LQR.
I. INTRODUCTION
The main task of a vehicle suspension is to
provide passenger ride comfort, safe road handling
together with an acceptable load capacity. Ride
comfort is achieved by isolating the chassis mass
from road disturbances while road handling is
achieved by preventing the wheels from loosing road
contact [1]. Load capacity depends on suspension
system deflection (suspension travel). A luxury
vehicle suspension will provide a high comfort level
but would significantly reduce the stability of the
vehicle at turns, lane change manoeuvres, or during
negotiating an exit ramp. On the other hand, a high
performance suspension system will yield good
vehicle handling, at the expense of ride comfort [2].
Generally, vehicle suspensions are classified into
three categories: passive, active and semi-active [3].
In passive systems, the vehicle chassis is supported
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by only springs and dampers with fixed parameters.
Passive means the system just dissipates kinetic
energy with no external energy input. In Semi-active
suspensions, no energy is supplied into suspension
system but the damper is a controllable, variable
damping one which is automatically adjusted based
on control strategy. For active suspension, the
damper and spring are interceded by a force actuator
which adds energy to the system in order to suppress
sprung mass oscillation of vehicle. The force
actuator can be controlled by various types of
controllers to achieve the desired performance [4],
[5].
A good design of an optimal passive suspension
can work up to some extent with respect to
optimized riding comfort and road holding ability,
but cannot eliminate this compromise [6]. Several
studies have shown that this conflict can be eased by
using active suspension systems instead of passive
ones. Demands for better ride comfort and good road
handling has motivated many automotive industries
to consider the use of active suspension systems.
However, although active suspension systems are
superior in performance to passive suspensions, their
physical realization and implementation is generally
complex and expensive, requiring sophisticated
electronically operated sensors, actuators and
controllers [2]. The actuator in an active suspension
system is controlled by various types of controllers
determined by the designer. The correct control
strategy should reduce the displacement and
acceleration of the sprung mass and provide
adequate suspension deflection to maintain tires on
contact with road and maximize load capacity. Thus,
the improvement of active vehicle suspension
systems via controller design has attracted more
interest and become a promising subject of research
and development in the last decade.
To simulate the performance of a suspension
system, three vehicle models can be used for
describing the dynamic behaviour, namely, quarter,
half and full vehicle models. Although a quartervehicle model (2-DOF) provides information on
vertical dynamics only, but because of its simplicity
and ability to provide useful insight into the
dynamics of the vehicle, it is used in much current
research studies on this topic [7], [8]. Half-vehicle
models (4-DOF) provide information on vertical
dynamics and lateral dynamics (rollover of vehicle)
[9],[10]. Full vehicle models (7-DOF) provide
information on vertical dynamics, lateral dynamics
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and longitudinal dynamics (pitch motion of vehicle)
[4], [11].
A number of active vehicle suspension control
strategies has been studied and/or proposed by
researchers. Agharkakli et al [3] investigated the
application of an LQR controller to an active
suspension system. The model used was a quarter
vehicle model. A single cosine and repeated cosine
bumpy profiles were input as road disturbances.
They concluded that active suspension systems
implementing linear quadratic regulator (LQR) gave
lower amplitudes and faster settling time for sprungmass displacement and acceleration, suspension
travel, and wheel deflection compared to passive
ones. However, performance was evaluated for a
discrete, limited single cosine bump but not for a
standard real road (ISO random road profile) which
is more representative and realistic [3]. Kumar [6]
tested the performance of an active suspension
system using a proportional integral derivative (PID)
controller whose gains are tuned using Zeigler and
Nichols tuning rules. A quarter vehicle model has
been used. A unit step and an ISO random road were
used as road disturbances. He reported that the PIDbased active suspension system improved ride
comfort but with no appreciable improvement in
road holding [6]. Changizi et al [12] compared the
performance of active suspension system using PID
and FLC controllers based on a quarter vehicle
model. A unit step input was used as road
disturbance. Their active suspension system using
the fuzzy logic control (FLC) controller performed
better than when using the PID controller. However,
road handling performance was not evaluated in
their work [12] . Sharkawy [13] compared the
performance of an active suspension system under
LQR, FLC and adaptive FLC controllers. A quarter
vehicle model has been used to investigate the
suspension behaviour under a unit step input and a
varying frequency sine wave as road disturbances.
He concluded that the performance quality in a
descending order was adaptive FLC, FLC and LQR
respectively[13]. Other control strategies such as
PID Controller tuned by Back Propagation Neural
Network [8], adaptive neuro active force control [14]
and Fuzzy logic controller optimized by genetic
algorithm [15] have been proposed for active
suspension systems.
In this paper, a quarter-vehicle model has been
used to simulate, evaluate and compare performance
of an active suspension system of a passenger
vehicle under three different proposed controllers.
These controllers are PID, LQR and FLC. Road
disturbances were modelled as three different
disturbance types: rectangular pothole, single cosine
bump and an ISO (class A) random road disturbance.
Comparison was made of system behaviour under
these controllers against each other and against the
original passive suspension system.
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II. SUSPENSION SYSTEM MODEL:
A 2-DOF quarter vehicle model has been used.
This model consists of a sprung mass representing
one quarter of total vehicle body mass and an
unsprung mass which refers to the mass of one
wheel assembly. Suspension system between sprung
and unsprung masses is modelled as a combination
of a linear viscous damper and a linear spring
element. Tire has been modelled by its equivalent
stiffness while tire damping is neglected. In the
proposed active suspension system, an actuator is
inserted between the sprung mass and the unsprung
mass, which is able to generate a control force that
plays important role in comfort and controlled
motion of vehicle. The Quarter vehicle model is
shown in Figure (1).
Fig.1: Quarter vehicle model a) passive suspension
system b) active suspension system
Applying Newton’s second law of motion, the
dynamic equations of motion could be derived as
[13]:
(1)
(2)
Let’s define the following state variables as:
Equations (1) and (2) can be arranged in state
space form as:
(3)
Where
,
,
Where Ms is the sprung mass, Mus the unsprung
mass, Cs the damping coefficient, ks the spring
stiffness, kt the tyre stiffness, ua the actuator force, zs
the sprung mass displacement, zus the unsprung mass
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International Journal of Engineering Trends and Technology (IJETT) – Volume 30 Number 2 - December 2015
displacement (both measured from static equilibrium
position) , zr the road profile, zs–zus the suspension
deflection (suspension travel) ,zus–zr the tire
deflection ,
the sprung mass velocity and
is
the unsprung mass velocity. Model parameters are
given in table(1) [6].
For optimal design the SVFB matrix K should
be selected such that the performance index J is
minimized [18] .
Linear optimal control provides the solution of
Equation (6). The gain matrix K is computed from
[1]:
Table1 Quarter vehicle model parameters.
(8)
Where the matrix P is determined by the solution
of Algebraic Riccati Equation (ARE) [2]:
Parameter
Sprung mass, Ms
Unsprung mass, Mus
Spring stiffness, ks
Tyre stiffness, kt
Damping coefficient, Cs
Value
290 kg
60 kg
16.8 kN/m
190 kN/m
1 kN.s/m
(9)
For proposed LQR controller, the parameters in
matrices Q and R were found by trial and error to be:
,
III. DESIGN DETAILS OF PROPOSED CONTROLLERS
1) PID controller:
Block diagram of the proposed active suspension
system using PID controller is shown in figure (2).
Fig. 1: Block diagram of the proposed PID controller
for active suspension system.
The control input U (t) is given by:
(4)
Where kp is the proportional gain, kd is the derivative
gain, ki is the integral gain and e (t) is the resulting
error. The PID controller was tuned using ZeiglerNichols rules [17].
2) LQR controller:
LQR is a technique in modern control theory
that uses state-space approach to analyse systems.
State-space simplifies analysis of a multi-output
system. In state variable form, mathematical model
of an active suspension system can be expressed as:
(5)
For optimal design of a state variable feedback
(SVFB ), we may define the controller’s
performance index, J as [3]:
(6) where Q and R in LQR denote weighting factors
or penalties for smooth trajectory(xTx)
and
minimal power consumption (uTu).
An SVFB regulator for a system is expressed as
R=0.01
Using the Matlab function (lqr) for solving ARE,
the value of the SVFB matrix k is:
3) FLC controller
A fuzzy control system is a system which
emulates a human expert. Creating machines to
emulate human expertise in control gives a new way
to design controllers for complex plants whose
mathematical models are hard to specify. The
knowledge of the human operator would be put in
the form of a set of fuzzy linguistic rules[19]. The
fuzzy logic controller consists of three steps:
fuzzification, fuzzy inference and defuzzification.
Fuzzification is a Process of defining the fuzzy sets,
and determination of the degree of membership of
crisp inputs in appropriate fuzzy sets. Fuzzy
inference is a process of evaluation of fuzzy rules to
produce an output for each rule and aggregation or
combination of the outputs of all rules.
Defuzzification is a process of conversion of
aggregate output fuzzy set to real-number (crisp)
output values [15].
The FLC used in this work has two inputs and
a single output. The two inputs are the suspension
travel (ZS-Zus) and the suspension velocity
. The output is the required actuator force
ua. This type of FLC is called fuzzy PD controller.
For the fuzzy inference step, product inference
technique has been used, while centre-average
method is used for defuzzification. The overall
structure of the proposed FLC controller is shown in
Figure(3) .Inputs and outputs are all normalized in
the interval of [−1, 1] by scaling variables with
coefficients of Ss, Ssv for inputs and Su for output
[11].
(7)
where K is the state feedback gain matrix.
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conducted for a vehicle speed of 16.67 m/s
(60km/hr).
1) Rectangular pothole road disturbance:
Response of vehicle suspension system using
proposed control to a sudden impact can be
investigated with simple rectangular pothole. The
pothole obstacle is mathematically modelled by the
function [20]:
Fig2: Block diagram of the proposed FLC
suspension controller.
Each input and output has five Membership
Functions (MFs). MFs of inputs and output are
negative big (NB), negative small (NS), zero (Z),
positive small (PS) and positive big (PB). The input
MFs are equally spaced in the universe of discourse,
and all MFs are described by a Gaussian function
with width σ=0.2.The output has five singletons
MFs having values of [-1 -0.5 0 0.5 1]. The rule base
is represented by 25 rules with fuzzy terms
derived from the designer’s knowledge and
experience knowledge related to the system. They
are listed in table (2) [13]. The rules of the fuzzy
controller can read as follows:
(10)
where A is the pothole amplitude, L is the pothole
length and s is the vehicle travelled distance (s=v*t).
In this work, the pothole has amplitude A of 0.05 m
and length L of 4 m. Rectangular pothole road input
is shown in figure(5).
Fig. 5: Rectangular pothole road disturbance
1.1) Ride comfort results:Table2: FLC rule base
Force ua
Suspension
Velocity
NL
NS
Z
PL
PS
Suspension travel (zs - zus)
NL NS
Z
PS
NL NL NL NS
NL NL NS
Z
NL NS
Z
PS
NS
Z
PS
PL
Z
PS
PL
PL
PL
Z
PS
PL
PL
PL
Normalized actuator force
Using these MFs and rule base, the output surface
of the fuzzy system is obtained as shown in figure
(4).
Fig. 6: sprung-mass displacement- pothole
disturbance.
1
0
-1
1
0.5
0
-0.5
-1
Normalized suspension velocity
-1
-0.5
0
0.5
1
Normalized suspension travel
Fig. 7: Normalized sprung-mass acceleration pothole disturbance.
Fig.4: Output surface of the fuzzy system
IV. RESULTS AND DISCUSSION:
In the present work, a quarter vehicle model of a
vehicle suspension system has been used to simulate,
evaluate and compare performance of three proposed
controllers, namely PID, LQR and FLC.
Performance has been compared for different road
disturbances against a passive suspension system.
The road disturbances used are a single rectangular
pothole, a single cosine bump and an ISO random
(class-A) road profile. Simulation has been
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Fig.8: sprung-mass jerk- pothole disturbance.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 30 Number 2 - December 2015
Table3: System recovery performance under different controllers.
(Pothole disturbance)
Controller
Settling
time, ms
FLC
557
PID
847
LQR
771
Passive
2648
Figure (6) depicts the sprung-mass displacement
response for different controllers. It can be
concluded from this figure that active suspension
resulted in a significant reduction in peak value of
sprung-mass displacement compared to the passive
suspension case, which is desirable for better ride
comfort. The best reduction of 23.8% was achieved
with FLC controller, followed by 14.9% for LQR
and 5.9% for PID. The FLC surpassed all other
controllers regarding recovery performance or
settling time as shown in table (3).
For sprung-mass acceleration, figure (7) shows
that active suspension also significantly surpasses
the passive case regarding peak acceleration values.
Still FLC has a best reduction achievement of 61.3%,
followed by 50% and 10.6% for PID and LQR
respectively. Moreover, except for the LQR
controller, sprung mass jerk or fluctuation of
acceleration has been appreciably reduced when
applying active suspension as shown in figure (8).
1.2) Road handling results:-
of total tire gripping force are shown in table (4).
This table shows that LQR produced the highest tiregripping margin of 51% of vehicle weight, followed
by PID (31%) and FLC (24.1%). However, best road
gripping force of (176% of vehicle weight) was
produced by FLC followed by PID (173 %) and
LQR (145%). Moreover, FLC has shown the fastest
and best recovery behaviour after leaving hole.
1.3) Load capacity results:-
Fig. 10: suspension travel- pothole disturbance.
Figure (10) shows suspension travel variation with
time. It is clear that, active suspension introduced an
appreciable improvement in rattle space utilization.
Note that a reduced suspension travel means higher
load capacity of vehicle. FLC produced the largest
reduction of (37.1%) compared to passive
suspension, followed by LQR (35.4%) and PID
(32.3%).
1.4) Actuator force results:-
Fig.9: Normalized dynamic tire load- pothole
disturbance.
Table 4: Best and worst tire gripping force values for different
controllers (pothole disturbance)
controller
Best gripping force,%
of vehicle weight
Worst gripping
force, % of vehicle
weight
passive
207.5
LQR
145
PID
173
FLC
176
7.4
51
31
24
Figure (9) represents the time response plot of
dynamic tire force normalized with respect to
vehicle weight. This force reflects the tire-road
gripping force. A higher gripping force means better
road handling and safety. Normalization with respect
to vehicle weight aims to sensing the magnitude of
this force and recognizing the case when tire
separation or jump occurs. This results in better
readability and interpretation of results. Figure (9)
shows that tire separation margin has been improved
with introduction of active suspension. Peak values
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Fig. 11: Normalized actuator force- pothole
disturbance.
The actuator control forces generated by
proposed controllers are compared in figure (11).
Peak values of normalized actuator control force
generated by FLC, PID and LQR are 77%, 98% and
111% of vehicle weight respectively. Therefore,
FLC requires the smallest actuator force when
implemented. Smaller force results in lower power
consumption, a more compact design and a more
realizable system.
2) A single cosine bump disturbance:
The single cosine bump input simulates a vehicle
coming out of a smooth obstacle. A single cosine
bump is mathematically given by [20]:
(11)
Where A is the bump height, L is the bump length
and s is the vehicle travelled distance (s=v*t). For
the present case, the bump has a height of 0.1 m and
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a length of 4 m. Bumpy road input is shown in
figure (12) [3].
Fig.12: A typical (single cosine bump) road
disturbance input.
2.1) Ride comfort results:-
values in transient portion were 8.8, 9.7 and 10.1 cm
for LQR, FLC and PID respectively. This is due to
instant fast response of controllers. However, it can
be concluded from this figure that active suspension
resulted in a significant reduction in settling time,
meaning fast recovery performance. The FLC
surpassed all other controllers regarding settling
time as shown in table (5).
For sprung-mass acceleration, figure (14) shows
that active suspension significantly reduces the peak
acceleration value. FLC has a best reduction
achievement of 40.2%, followed by 35.6% and
32.2% for PID and LQR respectively. Moreover,
sprung mass jerk has been appreciably reduced as
shown in figure (15).
2.2) Road handling results:-
Fig.13: sprung-mass displacement- cosine bump
disturbance.
Fig.16: Normalized dynamic tire load-cosine bump
disturbance.
Table 6: Best and worst tire gripping force values for different
controllers (cosine bump road disturbance)
Fig.14: Normalized sprung-mass accelerationcosine bump disturbance.
Fig.15: sprung-mass jerk- cosine bump disturbance.
Table 5: System recovery performance under different controllers.
(Cosine bump disturbance)
Controller
Settling time,
ms
FLC
466
PID
777
LQR
746
Passive
2950
Figure (13) depicts the sprung-mass displacement
response for different controllers. It can be observed
from this figure that sprung-mass displacement peak
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controller
passive LQR
Best gripping
209
218
force, % of vehicle
weight
Worst gripping
35.5
98
force, % of vehicle
(Tire
weight
separati
on)
PID
256
FLC
261
159
(Tire
separati
on)
130
(Tire
separati
on)
Figure (16) describes the time response plot of
dynamic tire force normalized with respect to
vehicle weight. It is clear from figure (16) that active
suspension implementation induced faster recovery
behaviour after leaving hole. FLC results in the
fastest and the best recovery behaviour followed by
PID and LQR. Peak values of tire gripping force are
shown in table (6). This Table shows that FLC
produced the highest best gripping force of 261% of
vehicle weight, followed by PID (256%) and LQR
(218%). It is noticeable that, for all active controllers,
when vehicle leaves top of bump tire separation is
observed. Therefore, if the system behaves passively
during the cosine bump interval, a better response is
expected. This means to delay the implementation of
active systems until the disturbance has passed.
Thereafter, the controller is implemented to suppress
oscillations produced by the bump disturbance.
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2.3) Load capacity results:-
Fig.17: suspension travel- cosine bump disturbance.
Figure (17) shows suspension travel variation
with time. It is clear that, active suspension
introduced an appreciable improvement in rattle
space utilization. Note that a reduced suspension
travel means higher load capacity of vehicle. FLC
produce the largest reduction of (36.7%) compared
to passive suspension, followed by PID (32.2%) and
LQR (25.3%).
(11)
where each sine wave is determined by its
amplitude and its wave number . By different
sets of uniformly distributed phase angles
in
the range between 0 and 2π .and, s is the momentary
position of vehicle. Amplitude of sine wave
calculates form:
(14)
Where
is wave number interval [20].
In this study, a road profile of class (A) was used
as input to system. According to equations (13&14)
road profile was generated by (N = 10) sine waves in
the frequency range from 0.628 rad/m to 6.283
rad/m. The amplitudes
were calculated and the
MATLAB function “rand” was used to produce
uniformly distributed random phase angles in the
range between 0 and 2π. Random road input is
shown in figures (19&20).
2.4) Actuator force results :-
Fig.19: Random road profile (ISO, class A)
Fig.18: Normalized actuator force- cosine bump
disturbance.
The actuator control forces generated by
proposed controllers are compared in figure (18).
Peak values of normalized actuator control force
generated by FLC, LQR and PID are 122%, 132%
and 165% of vehicle weight respectively. Therefore,
FLC requires the smallest actuator force when
implemented.
3) Random road profile disturbance:
Fig.20: Random road profile (ISO, class A), v=60
km/hr.
3.1) Ride comfort results:-
A random exciting function has been found
appropriate to model a real road surface as the main
characteristic of a random function is uncertainty.
The basic properties of random data in road model
are described by Power spectral density (PSD).
Random road profiles can be approximated by a
PSD function in the form of [21]:
(12)
Where Ω denotes the wave number in rad/m and
describes the value of PSD at reference
wave number =1 rad/m in m2/ (rad/m). The drop
in magnitude is modelled by waviness . By setting
waviness to =2, each class is simply defined by its
reference value . The ISO has proposed road
roughness classification (classes A-E) based on the
power spectral density values [2].
A random profile of a single track can be
approximated by a superposition of
sine
waves.
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Fig.21: Sprung-mass displacement- ISO class A road
profile.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 30 Number 2 - December 2015
Fig.22: Normalized sprung mass acceleration- ISO
road profile.
Figure (24) represents the time response plot of
dynamic tire force normalized with respect to
vehicle weight. Figure (24) shows that the tire
separation margin has been improved with
introduction of active suspension. Peak values of
Total tire gripping force are shown in table (7). This
Table shows that PID produced the highest margin
of 26% of vehicle weight, followed by FLC (28%)
and LQR (55%). However, best road gripping force
of (188.2% of vehicle weight) was produced by FLC
followed by PID (188.1 %) and LQR (147%).
Fig.23: Sprung mass jerk- ISO road profile.
The sprung-mass displacement for different
controllers is shown in figure (21). It can be
concluded from this figure that active suspension
resulted in an improvement in ride comfort due to a
significant reduction in peak values of sprung-mass
displacement compared to the passive suspension
case. The best reduction of 22% was achieved with
the FLC controller, followed by 5% for PID and
1%for LQR.
For sprung-mass acceleration, figure(22) shows
that active suspension also significantly suppresses
the peak and root mean square (R.M.S) acceleration
values. Still FLC has a best reduction in peak value
achievement of 76.6%, followed by 76% and 60.2%
for PID and LQR respectively. Also, FLC reduced
R.M.S value by 61%, followed by 59.3% and 52%
for PID and LQR. Moreover, sprung mass jerk has
been appreciably reduced as shown in figure (23).
3.2) Road handling results:-
3.3) Load capacity results:-
Fig.25: Suspension travel- ISO road profile.
Figure (25) shows suspension travel as a function of
time. Active suspension introduced an improvement
in rattle space utilization. FLC produce the largest
reduction of (61%) compared to passive suspension,
followed by PID (58%) and FLC (50%). Moreover,
FLC has a best reduction in R.M.S value
achievement of 52%, followed by 50% and 47.6%
for PID and LQR.
3.4) Actuator force results:-
Fig.24: Dynamic tire force- ISO road profile.
Table 7: Best and worst tire gripping force values for different
controllers (ISO road profiles)
controller
Best gripping
force, % of
vehicle weight
Worst gripping
force, % of
vehicle weight
Passive
215
LQR
147
PID
188.1
FLC
188.2
47
(Tire
separ
-ation)
55
26
28
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Fig.26: Actuator force- ISO road profile.
Comparison between actuator forces generated by
different controllers is indicated in figure (26). Peak
values of normalized actuator control force
generated by FLC, PID and LQR are 39.5%, 41.7%
and 63.3% of vehicle weight respectively. Also,
Actuator force R.M.S values were 22.4%, 23.6%
and 30.6% of vehicle weight respectively. Therefore,
FLC requires the smallest actuator force when
implemented.
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V. CONCLUSIONS
Three control strategies (PID, LQR and FLC)
have been tested for an active vehicle suspension
system to improve the ride comfort, load capacity
and road handling. A 2-DOF quarter vehicle model
is used to simulate suspension performance. Three
different road disturbances, namely, pothole, cosine
bump and ISO class A random road profile were
used to evaluate and compare suspension
performance implying different control strategies.
Simulation results showed that, active suspension
resulted in a significant improvement of ride comfort,
rattle space utilization and road safety. System
performance when implementing FLC proved to
surpass PID and LQR performance. FLC achieved
maximum reduction in peak values of sprung mass
acceleration for all road profiles followed by PID
and then LQR, which means that FLC produced the
best ride comfort performance. Moreover, The FLC
surpassed all other controllers regarding recovery
performance or settling time followed by PID and
then LQR. However, LQR gave the highest tire
gripping force (separation margin) followed by FLC
and then PID for all road profiles. FLC has the best
reduction in suspension travel for all road profiles
followed by PID and then LQR. Therefore, FLC
provided optimal utilization of rattle space. Another
advantage of FLC is that it requires the smallest
actuator force when implemented followed by PID
and LQR. Therefore, FLC implementation means
lower power consumption, a more compact design
and a more realizable system.
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